Finite Group Databasebeta

← Group #143650

Character table — Group #143650

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11112222224444444444888888888161616161616161616161616323232323232
order12224444442444888888816161616161616168888888816161616224444
χ111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-11-1
χ6111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1111-11
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-11-1-1-11
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1111-1
χ922222222222222-2-2-2-2-2-2-200000000220000-2-20000000000
χ1022222222222222-2-2-2-2-2-2-200000000-2-20000220000000000
χ1122222222-2-2-2-2-2222-222-2-200000000000000000000002-200
χ1222222222-2-2-2-2-2222-222-2-20000000000000000000000-2200
χ1322222222-2-2-2-2-22-2-22-2-2220000000000000000000002000-2
χ1422222222-2-2-2-2-22-2-22-2-222000000000000000000000-20002
χ15222222-2-2222-2-2-2222-2-22-22222-2-2-2-2000000000000000000
χ16222222-2-2222-2-2-2222-2-22-2-2-2-2-22222000000000000000000
χ17222222-2-2222-2-2-2-2-2-222-22000000000000000022-2-2000000
χ18222222-2-2222-2-2-2-2-2-222-220000000000000000-2-222000000
χ19222222-2-2-2-2-222-222-2-2-2-2200000000002i2i−2i−2i000000000000
χ20222222-2-2-2-2-222-222-2-2-2-220000000000−2i−2i2i2i000000000000
χ21222222-2-2-2-2-222-2-2-22222-2000000000000000000002000-20
χ22222222-2-2-2-2-222-2-2-22222-200000000000000000000-200020
χ232222-2-22222-22-2-2000000022−2−222−2−22-20000002−22−2000000
χ242222-2-22222-22-2-2000000022−2−222−2−2-22000000−22−22000000
χ252222-2-22222-22-2-20000000−2−222−2−2222-2000000−22−22000000
χ262222-2-22222-22-2-20000000−2−222−2−222-220000002−22−2000000
χ272222-2-2-2-222-2-222000000022−2−2−2−2220000002-22−2−22000000
χ282222-2-2-2-222-2-222000000022−2−2−2−222000000-22−222−2000000
χ292222-2-2-2-222-2-2220000000−2−22222−2−20000002-2−222−2000000
χ302222-2-2-2-222-2-2220000000−2−22222−2−2000000-222−2−22000000
χ314444-4-444-4-44-44-4000000000000000000000000000000000
χ324444-4-4-4-4-4-444-44000000000000000000000000000000000
χ3344-4-44-40000000000400-4000000000002-22-2000000000000
χ3444-4-44-40000000000400-400000000000-22-22000000000000
χ3544-4-44-40000000000-4004000000000002i−2i−2i2i000000000000
χ3644-4-44-40000000000-400400000000000−2i2i2i−2i000000000000
χ374-4-44004-400000022−22022−2200ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000000
χ384-4-44004-400000022−22022−2200−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000000
χ394-4-44004-4000000−22220−222200ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000000
χ404-4-44004-4000000−22220−222200−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000000
χ414-4-4400-4400000022−220−222200ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000000
χ424-4-4400-4400000022−220−222200−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000000
χ434-4-4400-44000000−2222022−2200ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000000
χ444-4-4400-44000000−2222022−2200−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000000
χ4588-8-8-8800000000000000000000000000000000000000000
χ468-88-800008i−8i0000000000000000000000000000000000000
χ478-88-80000−8i8i0000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.